Robust power detector for wideband signals among many single tone signals

ABSTRACT

Various technologies for isolating a signal of interest from signals received contemporaneously by an antenna are described herein. A time period for which a signal of interest is present in a second signal can be identified based upon ratios of values of the second signal to the mean value of the second signal. When the ratio of the value of the second signal at a particular time to the mean of the second signal exceeds a threshold value, the signal of interest is considered to be present in the second signal.

RELATED APPLICATIONS

This application claims priority to U.S. Provisional Patent ApplicationNo. 62/318,643, filed on Apr. 5, 2016, and entitled “ROBUST POWERDETECTOR FOR WIDEBAND SIGNALS AMONG MANY SINGLE TONE SIGNALS”, theentirety of which is incorporated herein by reference.

STATEMENT OF GOVERNMENTAL INTEREST

This invention was developed under Contract DE-AC04-94AL85000 betweenSandia Corporation and the U.S. Department of Energy. The U.S.Government has certain rights in this invention.

BACKGROUND

Antennas are deployed in many remote sensing, communications, and otherapplications in which characteristics of a signal of interest receivedby an antenna are used to identify characteristics of an environment,convey information, etc. In many cases, the environments in whichantennas are deployed for such purposes are also subject to noise andinterference from various sources of electromagnetic (EM) emission. Whennoise and interference are received contemporaneously with a signal ofinterest at an antenna, it can be difficult to isolate the signal ofinterest from the noise and interference in the output of the antenna.Identification of a time period during which the signal of interest ispresent in the output of the antenna can aid in processing of theantenna output to isolate the signal of interest. Conventionally, powerthreshold detectors that are tuned to specific characteristics of thesignal of interest and interfering signals in the output of the antennaare used to identify a time period during which the output of theantenna includes the signal of interest. Conventional power thresholddetectors therefore require advance knowledge of expected signalparameters of the interfering signals and the signal of interest.

SUMMARY

The following is a brief summary of subject matter that is described ingreater detail herein. This summary is not intended to be limiting as tothe scope of the claims.

Various technologies pertaining to a power threshold detector foridentifying a time period during which a signal (e.g., the output of anantenna) includes a signal of interest are described herein. In anexemplary embodiment, a plurality of signals is received at an antennasimultaneously over a period of time, wherein the plurality of signalsincludes the signal of interest. A data system receives the output ofthe antenna and outputs data indicative of the amplitude or power of theantenna output. For example, the data system can include ananalog-to-digital converter (ADC), and the ADC can output a plurality ofdigital values indicative of an amplitude of the antenna output at aplurality of times in the period of time.

A computing system receives the data from the data system and identifiesa plurality of times in the period of time for which the signal ofinterest is present in the output of the antenna. The identifying theplurality of times is based upon determining that a ratio of anamplitude of the antenna signal at the plurality of times to the meanamplitude of the antenna signal over the entire period of time exceeds apre-defined threshold value. In one example, the computing systemperforms an iterative process for identifying a plurality of times atwhich the signal of interest is present. In the iterative process, apeak value of the antenna signal is identified and a ratio of the peakvalue to the mean amplitude of the antenna signal is computed. If theratio exceeds the pre-defined threshold value, the computing devicestores the time corresponding to the peak value. The peak value is thenremoved from a plurality of values comprising the signal and anotheriteration of the process begins. An updated mean value of the signal iscomputed. A next-highest peak value is then identified, and a new ratioof the next-highest peak value to the updated mean value is calculated.If the new ratio exceeds the threshold, the computing device stores thetime corresponding to the next-highest peak value, removes thenext-highest peak value from the plurality of values comprising thesignal, and begins another iteration of the process. The processcontinues iteratively until the computed ratio in an iteration does notexceed the threshold, whereupon the process ends. The computing devicethen outputs an indication of a subset of the period of time of theantenna signal during which the antenna signal is likely to include thesignal of interest. The indication is output based upon the stored timescorresponding to the peak values identified in the iterative processdescribed above.

The above summary presents a simplified summary in order to provide abasic understanding of some aspects of the systems and/or methodsdiscussed herein. This summary is not an extensive overview of thesystems and/or methods discussed herein. It is not intended to identifykey/critical elements or to delineate the scope of such systems and/ormethods. Its sole purpose is to present some concepts in a simplifiedform as a prelude to the more detailed description that is presentedlater.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a functional block diagram of an exemplary system thatfacilitates identification of a time period for which a signal ofinterest is present in a signal received by way of an antenna.

FIG. 2 is a diagram of exemplary signal data for a plurality ofiterations of a process for identifying a time period for which a signalof interest is present in a received signal.

FIG. 3 is a flow diagram that illustrates an exemplary methodology foridentifying a time for which a signal of interest is present in a signalreceived by way of an antenna.

FIG. 4 is a flow diagram that illustrates an exemplary methodology foridentifying a plurality of times for which a signal of interest islikely to be present in a signal received by way of an antenna.

FIG. 5 is an exemplary computing system.

DETAILED DESCRIPTION

Various technologies pertaining to detection of an underlying signal ofinterest in a signal including noise and interference from other signalsare now described with reference to the drawings, wherein like referencenumerals are used to refer to like elements throughout. In the followingdescription, for purposes of explanation, numerous specific details areset forth in order to provide a thorough understanding of one or moreaspects. It may be evident, however, that such aspect(s) may bepracticed without these specific details. In other instances, well-knownstructures and devices are shown in block diagram form in order tofacilitate describing one or more aspects. Further, it is to beunderstood that functionality that is described as being carried out bycertain system components may be performed by multiple components.Similarly, for instance, a component may be configured to performfunctionality that is described as being carried out by multiplecomponents.

Moreover, the term “or” is intended to mean an inclusive “or” ratherthan an exclusive “or.” That is, unless specified otherwise, or clearfrom the context, the phrase “X employs A or B” is intended to mean anyof the natural inclusive permutations. That is, the phrase “X employs Aor B” is satisfied by any of the following instances: X employs A; Xemploys B; or X employs both A and B. In addition, the articles “a” and“an” as used in this application and the appended claims shouldgenerally be construed to mean “one or more” unless specified otherwiseor clear from the context to be directed to a singular form.

Further, as used herein, the terms “component” and “system” are intendedto encompass computer-readable data storage that is configured withcomputer-executable instructions that cause certain functionality to beperformed when executed by a processor. The computer-executableinstructions may include a routine, a function, or the like. It is alsoto be understood that a component or system may be localized on a singledevice or distributed across several devices. Additionally, as usedherein, the term “exemplary” is intended to mean serving as anillustration or example of something, and is not intended to indicate apreference.

With reference to FIG. 1, an exemplary system 100 that facilitatesdetection of an underlying signal of interest in a composite signalreceived from an operational environment 101 of the system 100 isillustrated. The system 100 includes an antenna platform 102 (e.g., anaircraft or other vehicle, a stationary antenna platform, etc.) on whichare mounted an antenna 104 and a data system 106. The system 100 furtherincludes a computing device 108 that receives data from the data system106. The computing device comprises a processor 110 and memory 112 thatcomprises instructions that are executed by the processor 110. Thememory 112 includes a signal isolator component 114 that identifies aperiod of time for which a signal of interest is present in a compositesignal based upon a ratio of a peak amplitude of the composite signal toa mean amplitude of the composite signal. Particularly when the signalof interest has a greater average amplitude than other signalscomprising the composite signal, the amplitude of the composite signalis expected to be high when the signal of interest is present relativeto when the signal of interest is not present.

The memory 112 also includes a signal processing component 116 thatperforms signal processing operations with respect to the signal ofinterest based upon the period of time identified by the signal isolatorcomponent 114. When signal processing operations are performed on acomposite signal that is time-limited to only those times that includethe signal of interest, a signal-to-noise ratio of an output of thesignal processing component 116 is increased relative to when thecomposite signal is processed over a period including times at which thesignal of interest is not present.

Operations of the system 100 are now described. The antenna platform 102operates in the operational environment 101. By way of example, if theantenna platform 102 is an aircraft, the operational environment 101 canbe an airspace through which the platform 102 is flying. In anotherexample, the platform 102 can be a fixed tower or other structure onwhich the antenna 104 is mounted, and the operational environment 101can be a region surrounding the fixed structure. The operationalenvironment 101 includes a plurality of sources of EM radiation 118a-118 m. The antenna 104 receives signals from the sources 118 a-118 msimultaneously, and outputs a composite signal to the data system 106,the composite signal comprising a superposition of the signals receivedfrom the sources 118 a-118 m, wherein the signal received from one ofthe sources 118 a-118 m is the signal of interest. The composite signalcan be considered to comprise the signal of interest and a third signalthat is a sum of all other signals received from the various sources 118a-118 m (wherein such signals include noise and interference).Generally, the third signal has a time duration that is longer than atime duration of the signal of interest. Systems and methods describedherein are well suited to identifying when the signal of interest ispresent in the composite signal when the third signal comprises aplurality of single-frequency tones within a bandwidth β and the signalof interest has a bandwidth less than or equal to β. The sources 118a-118 m can include EM emitters such as antennas, or the sources 118a-118 m can include objects that reflect EM radiation emitted by otherobjects.

Referring again to FIG. 1, the data system 106 receives the compositesignal output by the antenna 104. The data system 106 is configured tooutput composite signal data indicative of one or more characteristicsof the composite signal over a sample period of time. For example, thedata system 106 can include an ADC that digitally samples the analogcomposite signal and outputs a plurality of digital values indicative ofan amplitude of the composite signal at a corresponding plurality oftimes.

The computing device 108 receives the composite signal data generated bythe data system 106. Responsive to receiving the composite signal data,the signal isolator component 114 iteratively analyzes the compositesignal data to identify times in the sample period of time for which thesignal of interest is present in the composite signal. In an exemplaryembodiment, the signal isolator component 114 can begin by applying asmoothing filter to the composite signal data (e.g., a moving averagefilter). The smoothing filter applied by the signal isolator component114 is configured to reduce variance of the composite signal data, whichcan aid in reducing a likelihood that the signal isolator component 114will falsely identify a time as including or not including the signal ofinterest.

In each iteration, the signal isolator component 114 identifies amaximum value of the composite signal based upon the composite signaldata. The signal isolator component 114 also computes a mean value ofthe composite signal based upon the composite signal data. The signalisolator component 114 computes a ratio of the maximum value of thecomposite signal to the mean value of the composite signal. The signalisolator component 114 then compares the ratio to a predefined thresholdvalue. The signal isolator component 114 compares the ratio to thethreshold and determines whether or not the ratio is greater than thethreshold. If the ratio is less than or equal to the threshold, thesignal isolator component 114 can output an indication that thecomposite signal does not include the signal of interest at a timecorresponding to the maximum value. If the ratio is greater than thethreshold, the signal isolator component 114 can cause an indication ofthe time corresponding to the maximum value to be stored in the memory112. The signal isolator component 114 can then begin another iterationto identify another time where the composite signal includes the signalof interest.

A value of the threshold can be defined based upon a desired false alarmrate for the signal isolator component 114 in identifying times forwhich the signal of interest is present in the composite signal. Forexample, when the threshold value is lowered, it becomes more likelythat times identified by the signal isolator component 114 as times forwhich the composite signal includes the signal of interest do notactually include the signal of interest. Similarly, when the thresholdvalue is raised, it becomes more likely that times identified by thesignal isolator component 114 as including the signal of interest do, infact, include the signal of interest. The threshold value can further bebased upon a difference in average amplitude between the signal ofinterest and other signals comprising the composite signal.

In a subsequent iteration, the signal isolator component 114 updates thecomposite signal data to remove the maximum value from the compositesignal data. Thus, after the composite signal data is updated by thesignal isolator component 114, the updated composite signal data doesnot include the original maximum value identified by the signal isolatorcomponent 114 as described above. By way of example, and referring nowto FIG. 2, exemplary signal data 200 is shown for a plurality ofiterations 202-206 of a process executed by the signal isolatorcomponent 114, wherein the signal data 200 comprises a plurality ofsamples. The exemplary signal data in a first iteration 202 comprises aplurality of N samples. In updating the signal data 200 between thefirst iteration and a second iteration, the signal isolator component114 removes an identified maximum value of the first iteration of thesignal data 202. Thus, for example, if the maximum value of the firstiteration of the signal data 202 is the third sample, the signalisolator component 114 removes the third sample from the first iterationof the signal data 202 prior to the second iteration. In the seconditeration, therefore, the second iteration of the signal data 204comprises N−1 samples. A maximum of the updated signal data in thesecond iteration 204 is therefore a maximum of the remaining N−1samples. Likewise, the mean of the updated signal data in the seconditeration 204 is a mean of the remaining N−1 samples. As the signalisolator component 114 executes a plurality of M iterations, a maximumvalue is removed from the signal data 200 between each iteration. TheMth iteration of the signal data 206 therefore comprises N−M values.

Continuing the subsequent iteration, the signal isolator component 114computes an updated mean value of the updated composite signal data. Thesignal isolator component 114 then identifies a next-highest value ofthe composite signal, the next highest value being a maximum of theupdated composite signal data. The signal isolator component 114computes a new ratio of the next-highest value of the composite signalto the updated mean value of the composite signal. The signal isolatorcomponent 114 determines whether the new ratio is greater than thepredefined threshold. As before, if the new ratio is greater than thethreshold, the signal isolator component 114 causes an indication of thetime corresponding to the next-highest value to be stored in the memory112. The signal isolator component 114 then updates the composite signaldata again by removing the next-highest value, and computes anotherupdated mean value of the composite signal data. The signal isolatorcomponent 114 then begins another iteration of the process byidentifying another next-highest value of the composite signal basedupon the again-updated composite signal data. The process can becontinued until a predefined number of iterations is completed. Inanother example, the process can be continued until the signal isolatorcomponent 114 identifies that the ratio of a next-highest value to anupdated mean is less than the threshold value. By iterativelyidentifying times for which the signal of interest is present in thecomposite signal as described herein, the signal isolator component 114can more efficiently identify a subset of time for which the signal ofinterest is present in the composite signal than a system that analyzesall values of the composite signal data.

Responsive to identifying one or more times in the period of time forwhich the composite signal includes the signal of interest, the signalisolator component 114 can output data indicative of a subset of time inthe period of time for which the signal of interest is present. Forexample, the signal isolator component 114 can output data indicative ofthe one or more identified times. In another example, the signalisolator component 114 can output data indicative of a window of timefor which the signal of interest is present based upon an earliestidentified time and a latest identified time. The data indicative of thewindow of time can be data indicative of the earliest identified timeand the latest identified time.

The signal isolator component 114 can further identify a plurality ofwindows of time for which the signal of interest is present in thecomposite signal. For example, if the signal of interest is anintermittent signal, the signal of interest may be present from t₁ tot₂, absent from t₂ to t₃, and present again from t₃ to t₄, where t₁₋₄are times in the period of time of the composite signal. The signalisolator component 114 can be configured to identify the windows of timebased upon various criteria. Referring to the intermittent signalexample above, the signal isolator component 114 can identify that thesignal of interest is present from t₁ to t₂ based upon identifying thatthe signal of interest is present at t₁ and t₂ and determining that t₁and t₂ are less than a threshold amount of time apart. Continuing theexample, the signal isolator component 114 can identify that the signalof interest is absent from t₂ to t₃ based upon identifying that thesignal of interest is present at t₂ and t₃ but that they are greaterthan the threshold amount of time apart. The signal isolator component114 can then output data indicative of the identified windows of time.

It is to be understood that while in exemplary embodiments signals aredescribed as being received by way of an antenna, systems and methodsdescribed herein are applicable to other signals, such as signalstransmitted by wire connection, digital representations of signals, etc.

FIGS. 3-4 illustrate exemplary methodologies relating to identifyingtimes for which a signal includes another signal of interest. While themethodologies are shown and described as being a series of acts that areperformed in a sequence, it is to be understood and appreciated that themethodologies are not limited by the order of the sequence. For example,some acts can occur in a different order than what is described herein.In addition, an act can occur concurrently with another act. Further, insome instances, not all acts may be required to implement a methodologydescribed herein.

Moreover, the acts described herein may be computer-executableinstructions that can be implemented by one or more processors and/orstored on a computer-readable medium or media. The computer-executableinstructions can include a routine, a sub-routine, programs, a thread ofexecution, and/or the like. Still further, results of acts of themethodologies can be stored in a computer-readable medium, displayed ona display device, and/or the like.

Referring now to FIG. 3, a methodology 300 that facilitates identifyingthat a first signal includes a second signal of interest is illustrated.The methodology 300 begins at 302, and at 304 signal data is receivedthat comprises values of a first signal. The first signal is a signalthat comprises a second signal of interest and at least one othersignal. For example, the first signal can be a signal received by way ofa radar antenna, wherein the second signal of interest is an echo returnof the radar antenna and the at least one other signal is noise emittedby a radio antenna. The signal data can be a plurality of digitallysampled values of the first signal (e.g., as generated by an ADC) at aplurality of times in a period of time. At 306, a ratio of a first valueof the first signal to a mean of the values of the first signal isdetermined to exceed a threshold value. The first value can be, forexample, a maximum value of first signal. The threshold value can be apredefined value determined based upon a desired false alarm rate of asystem for identifying when the first signal includes the second signalof interest. From the ratio exceeding the threshold value it can beinferred that the first signal includes the second signal at a firsttime corresponding to the first value. At 308 data is output thatindicates that the first signal includes the second signal of interestat the first time based upon determining that the ratio exceeds thethreshold. In one exemplary embodiment, the data can be an indication ofthe first time. At 310 the methodology 300 ends.

Referring now to FIG. 4, a methodology 400 that facilitates iterativelyidentifying a plurality of times for which a first signal includes asecond signal of interest is illustrated. The methodology 400 begins at402 and 404 a peak value of first signal data is identified, wherein thefirst signal data is based upon the first signal (e.g., the first signaldata can be digitally sampled values of the first signal). At 406 aratio of the identified peak value to the mean value of the first signaldata is computed. At 408, a determination is made as to whether thecomputed ratio is greater than a threshold value. If the computed ratiois greater than the threshold value, the methodology 400 proceeds to410, whereupon a time corresponding to the peak value is stored (e.g.,in computer memory as data indicative of the time). At 412, the peakvalue identified at 404 is removed from the first signal data, whereuponat 414 the mean value of the first signal data is recalculated basedupon remaining values in the first signal data.

The methodology 400 then begins a second iteration, wherein at 404 a newpeak value of the first signal data is identified. Thus, in the seconditeration, at 404 a second-highest value of the first signal is the newpeak value of the first signal data. At 406 a new ratio of the new peakvalue to the recalculated mean value is computed, and at 408 it isdetermined whether the new ratio is greater than the threshold. If thenew ratio is greater than the threshold, the time corresponding to thenew peak value is stored at 410, the new peak value is removed from thefirst signal data at 412, and the mean is recalculated again based uponthe newly updated first signal data at 414. The methodology 400 thenbegins a third iteration. At 408, if the new ratio is not greater thanthe threshold, then an indication of times for which the first signalincludes the second signal of interest is output at 416 based upon thetimes stored at 410. Thus, the indication of times for which the firstsignal includes a second signal is based upon values of the first signaldata for which the ratio of the value to the mean of the first signaldata is greater than the threshold. The methodology 400 then ends at418.

Referring now to FIG. 5, a high-level illustration of an exemplarycomputing device 500 that can be used in accordance with the systems andmethodologies disclosed herein is illustrated. For instance, thecomputing device 500 may be used in a system that facilitatesidentification of times for which a signal includes a signal ofinterest. By way of another example, the computing device 500 can beused in a system that generates data indicative of a signal output by anantenna. The computing device 500 includes at least one processor 502that executes instructions that are stored in a memory 504. Theinstructions may be, for instance, instructions for implementingfunctionality described as being carried out by one or more componentsdiscussed above or instructions for implementing one or more of themethods described above. The processor 502 may access the memory 504 byway of a system bus 506. In addition to storing executable instructions,the memory 504 may also store signal data, times identified as beingtimes for which a signal includes a signal of interest, etc.

The computing device 500 additionally includes a data store 508 that isaccessible by the processor 502 by way of the system bus 506. The datastore 508 may include executable instructions, signal data, dataindicative of times for which a signal includes a signal of interestetc. The computing device 500 also includes an input interface 510 thatallows external devices to communicate with the computing device 500.For instance, the input interface 510 may be used to receiveinstructions from an external computer device, from a user, etc. Thecomputing device 500 also includes an output interface 512 thatinterfaces the computing device 500 with one or more external devices.For example, the computing device 500 may display text, images, etc. byway of the output interface 512.

It is contemplated that the external devices that communicate with thecomputing device 500 via the input interface 510 and the outputinterface 512 can be included in an environment that providessubstantially any type of user interface with which a user can interact.Examples of user interface types include graphical user interfaces,natural user interfaces, and so forth. For instance, a graphical userinterface may accept input from a user employing input device(s) such asa keyboard, mouse, remote control, or the like and provide output on anoutput device such as a display. Further, a natural user interface mayenable a user to interact with the computing device 500 in a manner freefrom constraints imposed by input device such as keyboards, mice, remotecontrols, and the like. Rather, a natural user interface can rely onspeech recognition, touch and stylus recognition, gesture recognitionboth on screen and adjacent to the screen, air gestures, head and eyetracking, voice and speech, vision, touch, gestures, machineintelligence, and so forth.

Additionally, while illustrated as a single system, it is to beunderstood that the computing device 500 may be a distributed system.Thus, for instance, several devices may be in communication by way of anetwork connection and may collectively perform tasks described as beingperformed by the computing device 500.

Various functions described herein can be implemented in hardware,software, or any combination thereof. If implemented in software, thefunctions can be stored on or transmitted over as one or moreinstructions or code on a computer-readable medium. Computer-readablemedia includes computer-readable storage media. A computer-readablestorage media can be any available storage media that can be accessed bya computer. By way of example, and not limitation, suchcomputer-readable storage media can comprise RAM, ROM, EEPROM, CD-ROM orother optical disk storage, magnetic disk storage or other magneticstorage devices, or any other medium that can be used to carry or storedesired program code in the form of instructions or data structures andthat can be accessed by a computer. Disk and disc, as used herein,include compact disc (CD), laser disc, optical disc, digital versatiledisc (DVD), floppy disk, and blu-ray disc (BD), where disks usuallyreproduce data magnetically and discs usually reproduce data opticallywith lasers. Further, a propagated signal is not included within thescope of computer-readable storage media. Computer-readable media alsoincludes communication media including any medium that facilitatestransfer of a computer program from one place to another. A connection,for instance, can be a communication medium. For example, if thesoftware is transmitted from a website, server, or other remote sourceusing a coaxial cable, fiber optic cable, twisted pair, digitalsubscriber line (DSL), or wireless technologies such as infrared, radio,and microwave, then the coaxial cable, fiber optic cable, twisted pair,DSL, or wireless technologies such as infrared, radio and microwave areincluded in the definition of communication medium. Combinations of theabove should also be included within the scope of computer-readablemedia.

Alternatively, or in addition, the functionally described herein can beperformed, at least in part, by one or more hardware logic components.For example, and without limitation, illustrative types of hardwarelogic components that can be used include Field-programmable Gate Arrays(FPGAs), Program-specific Integrated Circuits (ASICs), Program-specificStandard Products (ASSPs), System-on-a-chip systems (SOCs), ComplexProgrammable Logic Devices (CPLDs), etc.

What has been described above includes examples of one or moreembodiments. It is, of course, not possible to describe everyconceivable modification and alteration of the above devices ormethodologies for purposes of describing the aforementioned aspects, butone of ordinary skill in the art can recognize that many furthermodifications and permutations of various aspects are possible.Accordingly, the described aspects are intended to embrace all suchalterations, modifications, and variations that fall within the spiritand scope of the appended claims. Furthermore, to the extent that theterm “includes” is used in either the details description or the claims,such term is intended to be inclusive in a manner similar to the term“comprising” as “comprising” is interpreted when employed as atransitional word in a claim.

What is claimed is:
 1. A system, comprising: at least one processor; andmemory comprising instructions that, when executed by the at least oneprocessor, cause the at least one processor to perform acts comprising:receiving a first signal, the first signal based upon output of anantenna, the first signal taking a plurality of values over a period oftime, the first signal comprising a second signal of interest and athird signal, the second signal present for a subset of the period oftime; identifying that the first signal includes the second signal ofinterest at a first time in the period of time based upon determiningthat a ratio of an amplitude of the first signal at the first time to amean amplitude of the first signal over the period of time exceeds athreshold value; and outputting an indication of the subset of theperiod of time based upon the identifying that the first signal includesthe second signal at the first time.
 2. The system of claim 1, whereinthe third signal comprises a plurality of single-frequency tones.
 3. Thesystem of claim 2, wherein the plurality of single-frequency tones liewithin a first bandwidth, the second signal having a second bandwidththat is less than or equal to the first bandwidth.
 4. The system ofclaim 1, wherein the second signal has a greater average amplitude thanthe third signal.
 5. The system of claim 1, the acts further comprising:identifying that the first signal includes the second signal of interestat a second time in the period of time based upon determining that aratio of an amplitude of the first signal at the second time and themean amplitude of the first signal over the period of time exceeds thethreshold value; and wherein the outputting the indication of the subsetof the period of time is further based upon the identifying that thefirst signal includes the second signal at the second time.
 6. Thesystem of claim 5, wherein the indication of the subset of the period oftime comprises an indication that the subset is bounded by the firsttime and the second time.
 7. The system of claim 1, wherein identifyingthat the first signal includes the second signal of interest at thefirst time in the period of time comprises: identifying a maximum valueof the first signal, wherein the first time in the period of timecorresponds to the maximum value of the first signal; and determiningthat the ratio of the maximum value of the first signal to the meanamplitude of the first signal exceeds the threshold value.
 8. The systemof claim 1, the acts further comprising iteratively identifying that thefirst signal includes the second signal at a plurality of times in theperiod of time, and wherein outputting the indication of the subset ofthe period of time is based further upon the identifying that the firstsignal includes the second signal at the plurality of times in theperiod of time.
 9. The system of claim 8, wherein the plurality of timescomprises an earliest time and a latest time, wherein the indication ofthe subset of the period of time comprises an indication of the earliesttime and the latest time in the plurality of times.
 10. The system ofclaim 8, wherein iteratively identifying that the first signal includesthe second signal at a plurality of times in the period of timecomprises second acts of: a. computing a ratio of a maximum value of thefirst signal to the mean amplitude of the first signal over the periodof time; b. responsive to determining that the ratio of the maximumvalue of the first signal to the mean amplitude of the first signal isgreater than the threshold value, outputting data indicative of a timecorresponding to the maximum value; c. updating values of the firstsignal by removing the maximum value from the values of the firstsignal, wherein in subsequent iterations the maximum value of the firstsignal and the mean amplitude of the first signal are based upon updatedvalues of the first signal; and d. repeating the second acts of a, b,and c until the ratio of the maximum value of the first signal to themean amplitude of the first signal is less than or equal to thethreshold value; and wherein outputting the indication of the subset ofthe period of time is based upon the data indicative of the timescorresponding to the maximum values output at b.
 11. The system of claim1, the acts further comprising applying a smoothing filter to the firstsignal prior to identifying that the first signal includes the secondsignal at the first time.
 12. The system of claim 11, wherein thesmoothing filter is a moving average filter.